Method for safely and efficiently navigating magnetic devices in the body

ABSTRACT

A method of turning a medical device, having a magnetically responsive element associated with its distal end, at an operating point within an operating region inside a patient&#39;s body from an initial direction to a desired final direction, through the movement of at least one external source magnet. The at least one external source magnet is moved in such a way as to change the direction of the distal end of the magnetic medical device from the initial direction to the desired final direction without substantial deviation from the plane containing the initial direction and the desired final direction.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. patent application Ser. No. 09/678,640,filed Oct. 3, 2000, now issued U.S. Pat. No. 6,702,804, which claimspriority from U.S. Provisional Patent Application Ser. No. 60/157,619,filed Oct. 4, 1999, entitled “Method for safely and efficientlynavigating magnetic medical devices in the body”, the disclosures of allwhich are incorporated herein by reference.

FIELD OF THE INVENTION

This invention relates to a method for navigating magnetic devices inthe body, and in particular to a method for safely and efficientlynavigating magnetic devices in the body using a moveable source magnetoutside the body.

BACKGROUND OF THE INVENTION

The navigation of magnetic medical devices, such as magnet-tipped guidewires, catheters, endoscopes, or other instruments, with a movablesource magnet presents several difficulties in ensuring that themovement of the medical device is as the physician expects and intends.The difficulties arise for several reasons, including the lag betweenthe direction of the magnetic field applied by the magnet and the actualdirection of the tip of the medical device, and “coning” of the tip ofthe medical device as it deviates from the intended plane of the turn asit turns.

SUMMARY OF THE INVENTION

According to one aspect of the invention, navigation of a magnet-tippedmedical device takes into account the lag between the direction of themagnetic field applied by the source magnet and actual direction of themagnet tip. It is known that the magnet tip will lag the exact directionof the magnetic field at its location by some finite amount. This lag isthe result of a restoring torque due to the stiffness of the attacheddevice (e.g., the guidewire, catheter, endoscope, or other device towhich the magnetic element is associated).

This creates an ambiguity between the applied magnetic field and theactual direction of the magnet tipped device that can interfere withsafe and efficient navigation. The way this turn angle ambiguity isremoved is to provide a lead angle for the magnetic field which accountsfor the restoring, or turn-resisting, torque of the attached medicaldevice. According to one embodiment of this invention, information aboutthe restoring stiffness of the medical device to which the magnet isattached (e.g., a guidewire, catheter, endoscope or other device) isincluded in a computer program controlling the navigation. Informationof about the desired angle of turn and the desired radius (sharpness) ofthe desired turn can reside either in a lookup table or equationprogrammed in the computer. This information depends upon the propertiesof the device with which the magnet tip is associated, and thus will bedifferent for each different medical device. Given the magnitude of themoment of the tip magnet and this restoring torque, which is set equalto Γ, the value of B needed to achieve the required angle θ will follow.

According to a second aspect of this invention, it is desirable to maketurns in such a way as to maintain the magnet tip of the medical devicein the same plane as the initial direction and the desired finaldirection, avoiding the problem of “coning” in which the magnet tipswings out of the plane of the turn. This is particularly important whenthe navigation is through the parenchyma, although even when navigatingthrough body lumens, such as blood vessels, maintaining planarity duringthe turn can be important. While the movement of the source magnetusually accurately aligns the tip of the medical device in the desiredfinal direction, the movement of the magnet does not necessarily movethe tip in the desired plane.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a system for safely and efficientlynavigating in accordance with this invention;

FIG. 2 is an enlarged schematic diagram of the source magnet andpatient;

FIG. 3 is a schematic view of the source magnet, showing some of thefield lines;

FIG. 3A is a schematic view of the source magnet shown in FIG. 3 after arotation about Axis 2;

FIG. 4 is a schematic view of the source magnet with a polar coordinatesystem superimposed at the center of the source magnet;

FIG. 5 is a vertical cross-sectional view of the source magnet,illustrating the magnetic field directions useful for a turn in an axialplane;

FIG. 6A is a top plan view of the source magnet, illustrating themagnetic field directions useful for a turn from an axial plane at pointA in FIG. 5;

FIG. 6B is a top plan view of the source magnet, illustrating themagnetic field directions useful for a turn from an axial plane at pointB in FIG. 5;

FIG. 7A is a perspective view of a single magnet system having threedegrees of freedom, for implementing the method of the presentinvention;

FIG. 7B is a perspective view of the system shown in FIG. 7A with thesurface of constant magnetic field strength superposed thereon,illustrating some of the exclusion zones around which the magnet must bemaneuvered;

FIG. 7C is a perspective view of a single magnet system having fivedegrees of freedom, for implementing the method of the presentinvention;

FIG. 7D is a perspective view of the single magnet system shown in FIG.7C, from a different angle;

FIG. 7E is a side elevation view of the single magnet system shown inFIG. 7C, showing a work envelope in which the single magnet can moveabove a patient, around the end of the patient, and below the patient;

FIG. 7F is a side elevation view of the single magnet system showing themagnet behind the patient's head and showing clearance required for therotation of the single magnet;

FIG. 7G is a side elevation view of the single magnet system showing themagnet work envelope in which the single magnet can translate androtates, in an annulus around a patient's body, and the sweep volumerequired to accommodate rotations of the single magnet in the magnetwork envelope;

FIG. 7H is a side elevation view of the single magnet system showing thesource magnet rotated in cardiac to provide better access for the singlemagnet to the patient;

FIG. 7I is an end elevation view of the single magnet system showing thework envelope in which the source magnet can move in an annulus around apatient's head and showing the clearance between the work envelope ofthe magnet and the imaging system;

FIG. 8 is a schematic view showing the frames of reference of the sourcemagnet, the patent, and a locator device;

FIG. 9 is representation of the approximately spheroidal shape of asurface of constant field strength for a magnet having axial symmetry;

FIG. 10 is a diagram of a constant field strength surface showingseveral trial moves of the source magnet useful in visualizing theefficient movement of the source magnet;

FIG. 11 is a schematic view a patient and a source magnet, illustratingcoordinates and vectors useful in navigating;

FIG. 12 is diagram of the coordinates for the source magnet, shown inFIG. 11 illustrating the planes of rotation; and

FIG. 13 is a flow chart of the navigation inverse algorithm;

FIG. 14 is a cross sectional view of a typical coil source magnet 38showing a number of its magnetic field lines, and illustrating thegradient direction in two different locations;

FIG. 15A is a cross-sectional view of an aneurysm, showing the relativeorientations of an applied magnetic field and an applied magneticgradient before a gradient turn; and

FIG. 15B is a cross-sectional view of the aneurysm, showing the relativeorientations of an applied magnetic field and an applied magneticgradient after a gradient turn.

Corresponding reference numerals indicate corresponding parts throughoutthe several views of the drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In accordance with this invention , a magnetic medical device is safelyand efficiently navigated in the body using an externally appliedmagnetic field. The navigation system 20 for implementing the methods ofthis invention is shown schematically in FIG. 1 as comprising a computer22 having a keyboard 24, mouse 26 and joystick 28 for inputting thephysician's instructions. Of course not all of these input devices arenecessary, and other input devices can be used as well. A display 30 isalso connected to computer 22 to allow the physician to operate thesystem and monitor the navigation. Imaging apparatus 32 is connected tothe computer, which processes the signals and displays images of theoperating region on the display 30. A controller 34 is connected to thecomputer for controlling an articulation mechanism 36 that moves thesource magnet 38. The magnet 38 in turn creates a magnetic field in theoperating region 40 of the patient, and more particularly at theoperating point 42 in the operating region, to control the orientationof a magnetic medical device 44 having a magnet tip 46.

The magnetic medical device 44 may be any medical device that thephysician wants to navigate in the body, for example a guide wire, acatheter, an endoscope, etc. The medical device 44 has a magnet tip 46associated with it that is of sufficient size and shape to be responsiveto an applied magnetic field and/or gradient from the external sourcemagnet 38 for navigating the medical device. The magnet tip 46 may be apermanent magnet or a permeable magnet. In this description, it isassumed that the magnet tip 46 is a permanent magnet, with the magnetfield aligned along the longitudinal axis of the magnet. One of ordinaryskill in the art could readily adapt this invention for use withpermanent magnets of other configurations, or for use with permeablemagnets.

In general, the magnetic medical device 44 is located at a particularoperating point 42 within a larger operating region 40 in the patient.The operating region 40 is the region within the patient that theexternal source magnet 38 can apply a sufficient magnetic field toaffect the direction of the magnetic medical device 44.

The source magnet 38 may be a permanent magnet, but it is preferably anelectromagnet, and more preferably a superconducting electromagnet. Thesource magnet 38 may actually comprise more than one magnet. The sourcemagnet 38 is mounted on an articulation device 36 that can move themagnet 38. The articulation device 36 can translate and/or rotate thesource magnet. In the simplest case the articulation device might permittwo rotations of the source magnet, or perhaps two rotations of themagnet combined with a single translation, for example toward and awayfrom the patient. In the most elaborate case, the articulation devicemight permit two rotations of the source magnet, and three translationsof the source magnet in three mutually perpendicular directions.

The imaging apparatus 32, may be, for example, bi-planar fluoroscopyequipment for imaging the operating region 40. Bi-planar fluoroscopyallows the location and sometimes the location and the direction of themagnetic medical device 44 (or at least the distal end of the magneticmedical device) to be determined.

The invention relates to making a safe and proper turn efficiently. Aproper turn is defined as one in which the distal end of the magneticmedical device 44 remains in the plane containing the initial directionof the magnetic medical device and the desired final direction of themagnetic medical device. It is desirable to move the source magnet 38 insuch away as to effect the turning of the magnetic medical device 44 ina plane. There are typically a number of movements of source magnet 38that can turn the magnetic medical device 44 from a given initialdirection to the desired final direction. However, some of thesepossible movements will cause the magnetic medical device 44 to sweepout of the plane of the proper turn, in a motion known as “coning” thatcan unnecessarily disturb surrounding tissue. Others of these possiblemovements will be inefficient because of the significant movementrequired of the source magnet 38. Still others of these possiblemovements will be prohibited by practical considerations, such aslimitations on the rotation or translation of the magnet, interferencewith the equipment surrounding the magnet and the patient, imagingequipment, and imaging beams. It is important to select a magnet motionthat is both safe, i.e. causes a “proper” turn, and efficient, i.e. onethat is not unnecessarily of high complexity and long duration.

Lag from the Applied Magnetic Field

According to a first aspect of this invention, safe and efficientnavigation is achieved by taking into account the lag between the actualorientation of the medical device 44 and the orientation of the magneticfield applied by the source magnet 38. The magnetic torque vector isconventionally identified as Γ, and is given by the formula:Γ=m×B  (1)when m is the magnetic moment (a vector) of the magnet tip 46. Themagnitude of this torque is Γ=mB sin θ, where m is the magnitude of m, Bthe magnitude of B, and θ the angle between the vectors m and B. For apermanent magnet tip 46, with magnetization aligned in the usual wayalong its longitudinal axis, there is zero magnetic torque when themagnet tip is aligned exactly along B, and a maximum torque when themagnet tip 46 is perpendicular to (90 degrees away from) B.

Depending upon the size of a turn (or the radius of curvature at a pointin a continuous path) and the stiffness of the attached device, a leadtorque is needed to cause the magnet tip to turn in the correctdirection. Too much lead torque will turn the magnet tip too far, andtoo little lead torque will not adequately orient the magnet tip in theproper direction.

Where the magnet tip 46 is a permanent magnet, the moment m is fixedgeometrically, but where the magnet tip is a permeable magnet, themoment m will rotate to an intermediate direction between the fielddirection and the longitudinal axis of the magnet tip. Therefore,equation (1) will apply exactly to the moment, but only inexactly to afixed geometrical aspect, say the axis, of an elongated permeablemagnetic tip. This is because m shifts with B in a permeable magnet. Inthe remainder of this description, it will be assumed that the magnettip 46 is a permanent magnet magnetized along its longitudinal axis,unless otherwise specified. A person of ordinary skill in the art couldreadily calculate characteristics of a permeable tip moment, and usethem in a similar fashion.

In making a turn, whether manually or automatically with the aid of acomputer, the need for a lead torque must be anticipated. In oneembodiment of the present invention, information about the restoringstiffness of the medical device 44 to which the magnet tip 46 isattached (guidewire, catheter, endoscope, electrode, or other device) isincluded in the program controlling the navigation. Information aboutthe desired angle of turn and the desired radius (sharpness) of thedesired turn can reside either in a lookup table or equation programmedin the computer 22. This information depends upon the properties of themedical device 44 with which the magnet tip 46 is associated, and thuswill be different for each different medical device. Given the magnitudeof the moment of the magnet tip 46 and this restoring torque, which isset equal to Γ, the value of B needed to achieve the required angle θwill follow.

The desired angle of turn can be input, for example, using two point orthree point navigation methods such as those disclosed in co-pendingU.S. patent application Ser. No. 09/020,798, filed Feb. 9, 1998 entitled“Device and Method for Specifying Magnetic Field for SurgicalApplications”, incorporated herein by reference, or co-pending U.S.patent application Ser. No. 09/370,067 filed Aug. 6, 1999, entitled“Method and Apparatus for Controlling Catheters in body Lumens andCavities”, incorporated herein by reference.

Making a Proper Turn

According to a second aspect of this invention, safe and efficientnavigation is achieved by taking into account possible deviations of themagnet tip 46 of a medical device 44 between the initial direction andthe desired final direction caused by the movement of the source magnet38. Generally, the source magnet(s) 38 employed in magnetic navigationare designed so as to have fields which can be representedunambiguously. Moreover the articulation mechanism 36 for moving thesource magnets 38 is designed to maneuver a source magnet to a positionand orientation needed to apply the required field and/or gradient atthe operating point 42 where the magnet tip 46 is located. The sometimescomplex field shape of source magnet 38 generally demands a complexapproach to moving the source magnet to turn magnet tip 46, includingtranslation and/or rotation of the source magnet. However, knownsymmetries of the source magnet 38 can reduce its complexity, cost, andweight of the articulation mechanism. For example, the field of a commonsolenoid coil has complete symmetry about its longitudinal axis, andthus rotation about the longitudinal axis does not change the field atthe operating point in the patient. However, rotations about twomutually perpendicular axes that are perpendicular to the longitudinalaxis can provide any change needed in the orientation of the magneticfield at the operating point. In general these two rotations, combinedwith one or more simple translations for locational purposes, canprovide several alternate ways of changing the magnetic field vector atthe operating point. While these alternatives provide articulationflexibility, they also make calculation of specific navigation pathsdifficult.

It is convenient to focus on a coordinate system fixed in the frame ofreference of the source magnet 38, and view the (ultimately moving)position and orientation of the magnet tip 46 in the patient as it movesin this frame when the magnet is rotated. The essence of the desiredturn will be to move the source magnet 38 in the patient frame ofreference in a manner such that the magnetic field changes directionsmoothly and in the plane formed by the initial direction and thedesired final direction, i.e., the “proper turn” described above.

A first step in calculating a safe, efficient turn is the definition ofthe plane in which the magnet tip remains during the turn. This planecan be specified as a unit vector n perpendicular to it and determinedfrom the equationn=(V ₁ ×V ₂)/|(V ₁ ×V ₂)|  (2)i.e., a unit vector along the direction of the cross product of V₁ andV₂, where V₁ represents the initial direction and V₂ represents thedesired final direction.

The proper movement of the source magnet 38 may involve translationsand/or rotations. The method incorporating “Euler angles” is aconvenient and well-known tool for treating the rotations of an objectsuch as the source magnet. Goldstein, “Classical Mechanics” (SecondEdition), Addison-Wesley Publishing Co. (1980), incorporated herein byreference, describes matrix operations for keeping track of vectors insuch rotations. It is significant that these rotations are“noncommutative”, meaning that sequential rotations lead to a finaldirection which depends on the order of the individual componentrotations, i.e., the order of the rotations is important. Thisnoncommutative nature of rotational operations in mechanics must betaken into account when implementing rotations.

In the case of the static magnetic fields created by the source magnets38 preferably employed in this invention, the simplest possible rotationwhich will provide a proper turn is chosen. Even so, such a turn, madewith the simplest source magnet rotation and translation, but withoutfull regard for the magnetic field shape, could result in a magneticfield vector progression at the operating point 42 at the magnet tip 46which would lead to a turn with undesirable and possibly dangerousintermediate directions.

In FIG. 3, a source magnet 38, in the form of a simple coil, is shownwith a few of its field lines, which are symmetrical about itslongitudinal axis (Axis 1). The initial position and orientation of tipmagnet 46 is represented by vector V₁, and the desired final positionand orientation of the tip magnet after a 90 degree turn is representedby vector V₂ after the turn. Each point on each field line of sourcemagnet 38 is a magnetic field vector B, and each field line is in aplane that that contains the coil axis (Axis 1) and is referred to as an“axial plane.”

Once the direction or directions of the required magnetic field(s) areknown for a desired turn, a movement to cause the source magnet 38 toapply the required field at the operating point 42 is determined. Forsimplicity in describing this second aspect of the invention, it will beassumed that the magnet tip 46 will orient itself exactly along a fieldline at its location. This implies that the initial position before atum, and the desired final position after a turn, lie along a field lineof the source magnet 38. This assumption that V lies along B isimportant where, for example, the imaging system used to monitor theprocedure can only locate the position of the magnet tip 46, and not itsorientation. For simplicity in describing this second aspect of theinvention, it is also assumed that the magnet tip 46 is small enough tobe represented approximately by a vector at a point.

To illustrate the generally multiple sets of magnet motions that canaccomplish a given turn in a patient, FIG. 3 and 3A show two alternateways to rotate a field vector parallel to V₁ in a patient to a newdirection parallel to V₂ at essentially the same point in the patient.In FIG. 3 a translation of −V_(t) upward in the figure of the sourcemagnet 38 to relocate the operating point from B₁ to point B₃ willaccomplish this 90 degree turn of the field at a given point in thepatient.

In FIG. 3A the source magnet 38 is shown rotated clockwise 90 degreesabout Axis 2, which brings field point B₄ into a position parallel tothe desired direction V₂. It may or may not be necessary to translatethe source magnet 38 to bring the new location of B₄ to the startingposition of B₁, i.e., to the turning point in the patient.

The rotation and translation of the source magnet 38 preferably occursimultaneously, retaining the proper relationship between translationalspeed and rotational angular velocity, so as to maintain the fielddirection (with the magnet tip 46 crossing from field line to field lineof the source magnet 38 as necessary while the source magnet rotates andtranslates) so that the directional change of the field lines crossingthe region between point V₁ and point V₂ smoothly turn the magnet 46 asthe medical device 44 progressed in feeding the magnet tip forwardthrough the turn. If the turn is very sharp, the vectors would remainnearly at a point, and only change direction.

Depending on the capabilities of the articulation device for the sourcemagnet 38, one of the many possible movements (translation and/orrotation) of the magnet may be more efficient than the others. Forsimpler, less expensive articulation mechanisms, not all of the possiblemovements may be available. The selected movement can not always be themost efficient tum, and structural limitations of the magnet such asplacement of the cryocooler, power connections, etc., will sometimesprevent the use of the most efficient turn. In such cases a propermovement will not be the most efficient, but it should at least meet therequirement of maintaining the magnet tip in the plane of the turn.

As shown in FIG. 4, a spherical coordinate system is useful indescribing the position of the location of V₁ relative to the sourcemagnet 38. In this coordinate system, r is a vector from the center ofthe source magnet 38 to the operating point 42 (i.e., the location ofthe magnet tip 46); θ is the polar angle from the axis of the sourcemagnet (Axis 1) down to the line r; and φ is the azimuthal angle aroundAxis 1 of the plane of r and Axis 1, relative to an arbitrary fixedreference plane containing the axis. Because of axial symmetry of thefield of the source magnet, any motional change only in φ will result inno change in the field at V₁.

There are two types of planes in this coordinate system of significantusefulness in visualizing the coordinates and motions. The first typeare the axial planes, which are any planes that contain both the fieldline and the magnet axis. The second type are planes perpendicular tothe axial plane. When this second type of plane lies on the midplane ofthe magnet, it is referred to as the equatorial plane. Since rotationabout the axis of the source magnet 38 (Axis 1) does not change thefield at a point, a useful totally orthogonal system would have twoother axes perpendicular to the source magnet's axis (Axis 1) and toeach other. These axes are indicated as Axis 2 and Axis 3 in FIG. 4, andthey lie in the equatorial plane of the source magnet 38. Axes 2 and 3are shown schematically in FIG. 4, and could be physically implementedwith a gimbal apparatus to allow the source magnet to rotate about thesetwo axes. A usable articulation mechanism need only have two of thesethree axes, and it would still be capable of turning the coil to anyorientation, albeit with reduced freedom of intermediate motion.

A second major part of a turn is the calculation of the particularmagnet articulations for causing the magnetic field line(s) themselvesto execute the proper turn. For this action (which would preferably beimplemented with a computer program) there must either be an equation orlookup tables of the magnetic field for every possible orientation atevery point in the operating region 40 in the patient. An ideal dipole,a special magnet with a simple equation for its field, illustrates thispoint. It will be appreciated that a more realistic equation (or afinite-element equivalent calculation) will also retain the azimuthalsymmetry of this magnet). In the magnet coordinate system of FIG. 4,r=ix+jy+kz=i r sin θ cos φ+j r sin θ sin φ+k r cos θ, the field a dipoleis given byB=(μ_(o)/4π)[−(m/r ³)+3(m·r)r/r ⁵]  (3)where m is the moment of the dipole (now representing the source magnet38) and falls along the source magnet axis (by convention the z-axis), ris a vector between m (at the coil center) and the operating point inthe patient, and r is its magnitude. As shown in FIG. 4, m is locatedand aligned along the z-axis in the most efficient use of thatcoordinate system. The dot product m·r is then mr cos θ, where m is themagnitude of the magnetic moment.

With the magnet tip 46 located at r in the source magnet coordinatesystem and the initial vector directions and desired final vectordirections of the magnet field at that position, in both the sourcemagnet and patient coordinate systems, it is necessary during the turnto transform each incremental B in the source magnet coordinate systeminto B in the patient coordinate system while assuring that itsdirection remains in the plane of the proper turn. This can beimplemented with computer 22 having the full equation or a lookup tablewith an efficient search engine. The computer 22 must first establishthe location and orientation of the magnet tip 46 in the magnetcoordinate system, i.e., V₁. Then it must establish V₂ in thiscoordinate system, and the plane of rotation n_(a). This navigation willnow be described in more detail.

Two prototypical cases establish that any turn where the magnet tip liesalong a field line can be made through a combination of translations androtations. In both of these cases the magnet tip starting position isalong a field line, and therefore in an axial plane. In the first suchcase, both V₁ and V₂ are oriented in an axial plane, and in the secondcharacteristic case V₁ is oriented in an axial plane and V₂ isperpendicular to that plane. All other possible turns where the magnettip initially lies along a field line can be considered as somecombination of these two special cases, with appropriate trigonometricprojections.

First Prototypical Case

In the first case where V₂ lies in a plane containing the axis or thesource magnet 38 (Axis 1) and V₁, then a rotation in that pane, whichcan be called the “starting plane” is necessary for a proper turn. Asnoted above, the vector direction of any plane is a vector of unitlength which is perpendicular to the plane. Rotation in this plane is arotation about a virtual axis perpendicular to that plane. This virtualrotation axis n_(a) is defined by analogy to equation 2:n _(a)=(V ₁ ×V _(a))/|(V ₁ ×V _(a))|,  (4)where V_(a) is a vector along the axis of the source magnet 38. Thisplane is chosen for convenience because it contains V₁, and it ismagnetically the same as any other plane containing the axis of thesource magnet 38. Therefore a vector V₁ located in a plane at anyazimuthal angle φ will satisfy equation (4) for this case. However, onlyrarely will n_(a) happen to be parallel to Axis 2 or Axis 3 of FIG. 4.Instead, the most general rotation can be formed from a trigonometriccombination of rotations about these two axes. For example, if the axisn_(a) were found in one case to be 45 degrees clockwise (looking down onthe coil) from Axis 2, it would mean that the front of the coil betweenAxis 2 and Axis 3 would tilt up to perform a clockwise rotation aboutthe n_(a) axis. Looking toward these axes, Axis 2 would rotatecounterclockwise, and Axis 3 would rotate clockwise (looking along thisunit vector). In this case, both axes would rotate at the same angularrates.

FIG. 5 illustrates this turn in an axial plane (with V₁ and V₂ separatedby an exaggerated distance). The starting point is labeled A, and B andC identify two other points around that field line which passes throughA. For clarity, only a single field line is shown. (The circular shapeshown for the field line is not intended to be a highly accuraterepresentation of the shape of a field line from a real coil.) The planeof turn, designated by n_(a), is oriented out of the page.

The field line at point B is parallel to V₂, and a simple translation ofthe source magnet 38 to bring point B to the location of V₂ wouldaccomplish a turn of the magnet tip 46 in the patient. However, thetranslation would have to be judiciously chosen on some curve in orderfor the field strength to remain unchanged during the turn. It isdesirable that the field strength remain constant to reduce variationsin the direction of the magnet tip 46. Moreover, the translational pathshould lie in the starting plane. With these choices, the turn would bea proper one, albeit probably not efficient. To accomplish this turn,the translational path would be determined by moving from point A topoint B in the field line of equation (3) or an accurate line calculatedfor a real coil, and then translating the source magnet in the inversedirection of that path. To maintain the curve as a proper turn wouldinvolve a choice of fixed φ. An obvious choice for an efficient(although perhaps not the most efficient) proper turn in this case wouldbe a translation with φ and magnitude B fixed at each step of the turnand with θ changing smoothly and monotonically.

Second Prototypical Case

In the second prototypical case, V₁ is in an axial plane but V₂ isperpendicular to that plane so that rotation about a different virtualaxis n₂ is necessary. Since n_(a) still defines the starting plane, thevector axis of rotation, n₂, is perpendicular to both V₁ and n_(a)n ₂=(V ₁ ×n _(a))/|(V ₁ ×n _(a))|  (5)

Two turns for this second general case are illustrated in FIGS. 6A and6B, which are views looking down on the axis of the source magnet 38. Afirst turn of the second prototypical case is illustrated in FIG. 6Awhere the starting location is shown as a projection of point A of FIG.5 onto this view. The field rotation is shown as n₂, out of the paper.

It is apparent that a pure rotation of the source magnet 38 about itsaxis, needed to accomplish n₂, cannot be effective for this proper turnbecause of field line symmetry. A translation, approximately along Axis3 and in direction T, would bring the magnet tip 46 to point A′ in theframe of reference of the source magnet 38, as shown by the straightdashed line, and would accomplish a proper turn. However, since thedistance between the path and the source magnet axis varies, the fieldstrength will vary during such a turn. Instead, a translation of thesource magnet 38 in which point A progressed in a circle around thesource magnet axis, would result in a proper turn with constant fieldmagnitude. Such a path is shown as a dot-dashed line 50. (This is thetrajectory of the magnet tip 46 in the frame of reference of the sourcemagnet. The movement of the source magnet 38 in the operating room willbe opposite to this motion and is show as dot-dashed line 52).

A second turn of the second prototypical case is illustrated in FIG. 6B,where V₁ is again in the axial plane, but now is located as point B ofFIG. 5, i.e., pointing into the paper in this view. Now n₂ points awayfrom the coil. This turn is the simplest, and is accomplished purely byrotating the coil about the axis from the center of the magnet out tothe location of V₁. For generality, this is shown as different from Axis2 or Axis 3. Such an axis is established trigonometrically in the samemanner as described above. (A prior pure rotation about the coil axiscould establish one of these as the turn axis without disturbing themagnet tip, but with some simpler articulation mechanisms, such arotation might have been considered generally unnecessary and thereforenot available).

Having established the qualitative nature of proper turns, we nowdescribe quantitative means of calculating the magnet articulationsneeded for navigation. Navigation in the operating region of the patientwould intuitively seem to be most directly visualized and calculated inthe patient reference system. This would, however, entail transformationof the rotating and translating magnetic source field into thatreference system, which would be difficult, given that the source magnetfield often cannot be put into analytical form. (A lookup table of fivedimensions could contain all transformations to follow, but is just amodification of the following method). While transforming a field fromone frame of reference to another can be complex, any specific magneticfield vector is easily transformed between the coordinate systems. Thismethod has been devised to avoid the difficulty of fieldtransformations. It provides ways to test trial turns for propercharacteristic, and to break up a full turn as necessary to maintain theturn in a sufficiently close planar form. In addition, an essentialfeature in this method is a means of removing the ambiguity of a turn,i.e., a method of limiting the possibilities to a small, practical“neighborhood” of trial turns, and then choosing the “best” proper turnfrom among the possible trial turns.

The procedure works in the reference frame of the source magnet afterthe desired vector in the patient coordinate frame is transformed, andthen calculates and transforms each necessary field vector into thepatient frame. Sometimes this can be done automatically with searchmethods and equations. The procedure can involve steps in purelyrotating a field vector through a turn from V₁ to V₂ in the patientframe, using operations in the source magnet frame, and taking care thatthese operations take into account when a rotation in that frame will inaddition require a translation of the source magnet 38 in the patientframe. For the method to work, the relationship between the two framesmust be known. An external locating means can be provided to connect thelocation and orientation of the frame of reference of the source magnetto the patient frame. One example of such a locating means is disclosedin Van Steenwyk et al., U.S. Pat. No. 4,173,228, issued Nov. 6, 1979,for Catheter Locating Device, incorporated herein by reference. In thefollowing description, and as shown in FIG. 8, unprimed coordinates (x,y, z) will designate the patient frame, and primed coordinates (x′, y′,z′) are in the source magnet frame. Third, coordinates (x″, y″, z″) areused for the room coordinates, i.e., the coordinates in which thelocator device is fixed. In one embodiment, the locator deviceestablishes the relationship between the magnet tip on the medicaldevice and the source magnet, as described above. In another embodiment,the locator device might establish the relationship between the sourcemagnet and a point on a patient, fixed in the room, in which case theorientation of the magnet tip 46 would have to be determined in someother way. Bi-planar fluoroscopic imaging can locate the magnet tip 46,but does not always give good information about its orientation.Commercial magnetic field locators are available which can also find theorientation of the magnet tip 46. Other imaging systems can usecombinations of imaging modalities. In the following discussion, anyappropriate locating and/or imaging devices can be used.

Generally, the transformation problem has five degrees of freedom(although, depending upon the application, it is not necessary that thearticulation device must have all of these degrees of freedom). Thetranslation of a vector between two reference frames has 3 components,and the rotation of a vector has 2 components (polar and azimuthalangles). The field vectors to be transformed need not be rotated aroundan axis which is collinear with their own directions.

Two types of vectors have been discussed. Vectors which yield theposition of an object in a reference frame, and vectors which describe amagnetic field at a point. These are treated separately and explicitlybelow.

The operating position location in each frame of reference can bespecified as a vector relative to the origin in that frame of reference,and a positional transformation in a given frame is then a vectoraddition or subtraction. (There is no need to rotate the positionvectors except when dealing with exclusion zones.) However, the fieldvectors must in general be rotated and translated. In the patient frame,the location vector is simply a vector from a fixed origin in that frameout to the operating point (where the magnet tip 46 is located). In theframe of the source magnet 38, however, the origin for the locationvector will change each time the source magnet is translated, asdescribed below. FIG. 8 shows frame axes in these frames plus thelocator frame. With some location methods, the origin of the patientframe could be at the operating point 42 where the magnet tip 46 islocated, and would move as that point moved. A locator system operatingthroughout the duration of the procedure would maintain informationabout the locations of (0, 0, 0) and (0′, 0′, 0′) relative to its ownfixed frame (0″, 0″, 0″).

The location and direction of vector V₁ in the frame of reference of thepatent is transformed into V₁′ in the frame of reference of the magnetsource 38 by well known vector algebraic methods. In general this willrequire separate vector translation and rotation operations.(Translations involve vector sums or differences, rotations involvematrix multiplication.) Given V₁, the three coordinates of the positionof the vector V₁′ are found by simple addition of the known coordinateorigin transformation from (0, 0, 0) to (0′, 0′, 0′). The neededinformation is known, as stated above, from external locating means. Ofcourse, if the external locating means is operating continuously, thisstep will be immediate and trivial. Otherwise, any magnet movement androtation since an initial “calibrating” relative location andorientation by that locating means will necessarily have been recordedin the processor and will be accounted for. In either case, one morestep is necessary. The vector V₁′ must be located relative to (0′, 0′,0′), and its orientation must also be found. If V₁ is the very firstvector in the procedure V₁, will be found in the calibration justmentioned. Otherwise, V₁ will be known in the processor, which mustcontinually account for each step of a procedure, and within certainaccuracy can retain a “dead reckoning” of translations and rotations ofthe source magnet 38, as well as translation and rotation of the magnettip 46.

It is sometimes necessary and usually desirable in navigation for themagnetic field strength to remain constant. This provides a usefulconstraint on the navigation calculations. One of ordinary skill in theart would know how to change the magnetic field strength, if needed,given this method for a turn made at constant field strength. In theconstant field strength method, the location of V₁′ would always fall ona surface of constant field strength. For a typical single sourcemagnet, such a surface would be calculable, and would approximate anaxially symmetric spheroid.

FIG. 9 illustrates a surface 100 of constant field strength for a sourcemagnet 38, along with a few vectors 102 on each of several “latitudeplanes” 104. It is seen that on a given latitude plane the axialsymmetry of the magnet assures that the field line vectors 102 make aconstant angle with the surface 100, and also with the magnet axis. Eachfield line lies in a plane which contains the magnet axis. Thus changesin field direction, on the constant field surface, require somecomponent of motion along a longitudinal line.

Once the relative locations of V₁ and V₁′ are determined, rotations aremade in the “forward direction,” V₁ to V₁′, by standard matrix means.For example, Goldstein equation (4-46) shows such a transformation usingEuler angles (φ, θ, ψ) in one turn sequence convention. This referencealso discusses several other such conventions. The particular rotationconvention used for (φ, θ, ψ) in this invention is arbitrary, but oncechosen for the initial calibration it must be retained. A convenientchoice might use the axes of rotations provided by the articulationmechanism. “Reverse” rotations, say from V₁′ to V₁, are then given by aninverse matrix, Goldstein equation (4-47). It is to be understood thatthe angles (φ, θ, ψ) are not angles through which the source magnet willactually turn, but rather are used in the algorithm to calculate thetransformation between a vector in the two reference frames. Instead,the actual magnet turns will consist of simple small vector rotations,with added translation if needed to maintain the vector position of themagnet tip 46 in the patient frame.

The movements of the source magnet for a proper turn are preferablyfirst carried out “virtually” in a computer processor 22. Once the pathfor the movements of the source magnet is determined, execution of thepath will require instructions to the controller 34 of the magnetarticulation mechanism 36. Algorithms for calculating the angles andtranslational position of the magnet needed to provide a next V (i.e., anext B) are described below:

A. Once V₁ is located, the desired turn to V₂ is input by the physicianaccording to one of the standard means of communicating to the processorsystem. Examples of methods of inputting desired turns are disclosed inU.S. utility patent application Ser. No. 09/020,798, filed Feb. 9, 1998entitled “Device and Method for Specifying Magnetic Field for SurgicalApplications”, incorporated herein by reference, or co-pending U.S.patent application Ser. No. 09/370,067 filed Aug. 6, 1999, entitled“Method and Apparatus for Controlling Catheters in Body Lumens andCavities”, incorporated herein by reference.

B. The movement of the source magnet to effect the turn from V₁ to V₂ isdetermined. This is conveniently done with a computer processor. Theangle by which the direction of the magnet tip 46 varies from the planecontaining V₁ and V₂ is then determined. If this amount does not exceeda predetermined threshold for acceptable deviation, e.g., 5 degrees,then the articulation mechanism 36 can be operated by controller 34under the direction of the computer processor 22 to make the determinedmovement of the source magnet 38. If the turn from V₁ to V₂ is small,for example, 10 degrees or less, it is likely that only one step of theturn is needed, as any coning during the turn will be small enough thatit generally will not interfere with navigation. However, if the amountby which the direction of the magnet tip 46 varies from the plane of V₁and V₂ by more than the predetermined threshold, then the turn is brokenup into a number of sub-tums. Of course, sub-tums could be usedautomatically, without testing whether they are needed.

C. If subtums are employed, the final vector V₂ is labeled V_(n), and anumber of intermediate vectors V_(I) (i=2, 3, . . . , n−1) aredetermined by the processor 22. One method of determining theseintermediate vectors is to make an even-sized division of the angle ofturn, constraining each individual vector to be in the plane formed byV₁ and V_(n). Other methods of determining these intermediate vectorsinclude unequal divisions of the turn angle based upon where the magnettip direction deviates from the desired plane of the turn by more thanthe predetermined threshold, or some lesser value. Of course there arenumerous other methods for determining the intermediate vectors.

D. The vectors V₁, V₂, . . . , V_(n) in the patient frame of referenceare transformed to V₁′, V₂′, . . , V_(n)′ in the source magnet frame ofreference by a pure forward rotation. In general, V₁′, V₂′, . . . ,V_(n)′ will not lie in a plane, even if V₁, V₂, . . . , V_(n) did. Eachpair of angles, V₁′, V₂′, or V₂′, V₃′, etc. will form a plane, which canbe determined as in equation (2) above. Resulting rotations V₁ to V₂, orV₂ to V₃, etc. will not generally lie in a single plane, but since theseare small rotations they will have acceptable individual coning, bydecision of step 2 above. Choice of the starting vector in the patientplane, however, will assure that the overall turn is nearly planar.

E. The processor 22 then determines a movement of the magnet for each ofthe sub-turns. When the magnet makes a rotation from V_(i) to V_(i+1),the point on the constant field surface will in general move, i.e.,translate relative both to (0′, 0′, 0′) and to (0, 0, 0). Also, themagnet rotation needed to make this small turn, will not in general beuniquely determined, which is common with inverse problems. Theprocessor will calculate such a translation for the small angle rotationV_(i) to V_(i+1), using a series of trial rotations in a plane tangentto the surface at the initial point, in the neighborhood of the vectorV_(i), as shown in FIG. 10. In general, each vector associated with arotation shown in this frame, corresponds to a rotation and translationof the point in the patient reference frame. That is, as the fieldvector position in the magnet frame changes from P_(i) to P_(i+1) due torotation in the magnet frame, the reverse transformed position in thepatient frame will need in addition to translate if the originalrotation in the patient frame [Goldstein equation (4-46)] is totransform back correctly. That means that the source magnet 38 mustsimultaneously be translated to maintain the magnetic field vectorposition constant in the patient frame. Only moves with some componentalong a longitude line will change the field vector direction. However,it will sometimes be found that the most efficient step for a small turnwill also have some component of rotation along a latitude line, whenaccount is taken of the transformation into patient coordinates. Foreach trial the processor will calculate the translation inferred in thepatient frame. For the trial chosen as optimum, the magnet will have tomake the inverse of this translation, in order to keep the vectorlocation fixed in the patient frame.

F. The processor selects from the trial rotations one which is mostefficient, i.e., the trial which requires the smallest translation ofthe magnet to accomplish the (partial) turn in the patient frame withouta translation in the patient frame. A weighting algorithm can bedeveloped based upon the “costs” of certain rotations over otherrotations, certain translations over other translations, and ofrotations over translations.

Practical articulators and magnet systems will have limited rotations,say 360 degrees or 720 degrees, because of leads, and other attachments.They also will have limitations of motions because of interference ofthe magnet and its accoutrements with the patient, with imagingequipment and imaging beams, or with other medical equipment. Suchlimitations can be transformed from the patient reference frame to thesource magnet reference frame and entered into the processor 22controlling the navigation as an exclusion region. Preferably thelimitations can be entered as a series of vectors X₁,X₂, . . . ,X_(n)describing a surface in the patient frame, which transform to X₁′,X₂′, .. . X_(n)′ in the source magnet frame. These can be chosen withsufficiently small angular spacing as to provide a means of forming asmooth sheet of exclusion boundary in the magnet frame, which is used bythe processor to execute limits on magnet motion.

When the magnet housing and accoutrements present a highly asymmetricalfront toward the patient and interfering equipment, the exclusion sheetwill be dynamic, i.e. a joint overlap of sheets for the patient regionand for the magnet region will be needed to prevent interference.

G. The final and all intermediate step vectors (V₂′, . . . V_(n)′) willbe calculated before the execution of a turn. When, in any turn, thefinal (or any intermediate) step vector falls beyond an exclusion limit,or near it, the processor 22 can choose to reorient the source magnet,using its symmetry, if helpful, to move safely away from incursion ofthe limit. Clearly, for safety the limit surface can have been chosenconservatively “inside” a true limit surface.

H. The processor 22 also confirms that the rotations will not cause thedirection of the magnet tip to vary from the plane of V₁ and V_(n) bymore than the predetermined threshold. If it does, the processorreselects some or all of the intermediate vectors (V₂′, . . . V_(n−1)′),and repeats the process.

I. The processor 22 will then cause the articulating mechanism 36 toturn and/or translate the source magnet 38 successively through theangles from V₂′ . . . , V_(n)′, which will turn the angle in the patientfrom through V₂, . . . V_(n−1) to V_(n).

Common matrix transformations can be used for conversion between thepatient reference frame and the source magnet reference frame. Onetechnique includes the steps of:

1. Characterize the field of the source magnet 38 by measuring it overthe sample volume of interest at sufficient resolution thatinterpolation will not yield significant errors.

2. Putting the source magnet field information into a computer functionB_(m)(x_(m),y_(m),z_(m)) (x′, y′, z′ as shown in FIG. 8), or equivalentlookup table, where x_(m), y_(m), and z_(m) are expressed in magnetcoordinates and B_(m) is the magnetic field vector.

3. Compute the transformation matrix T_(mp) for converting a generalvector B from magnet to patient coordinates.

4. Invert this matrix to T_(mp) ⁻¹.

5. Compute x_(m), y_(m), z_(m) by feeding T_(mp) ⁻¹ into a generalminimization function that moves around the magnet on its constraints(e.g., where there are three degrees of freedom, 2 rotations and 1translations) and using a forward calculation function:B _(p)(x _(p) ,y _(p) ,z _(p))=T _(mp) ⁻¹ B _(m)(x _(m) ,y _(m) ,z _(m))Such a routine would rapidly converge unless the magnet shape and/orshielding presented fields which are pathological (not monotonic in thevicinity of the required components). Such magnet designs should beavoided. Where there are more degrees of freedom, this will involvesearching over the surplus degrees of freedom to minimize the requiredmovement (rotation and translation) of the source magnet.

Navigating with a Single Magnet

When the determination of magnet rotations for a safe turn has been madeby the previously described steps, instructions to the chosen roboticarticulation mechanism 36 for magnet positions and rotations to beachieved in a turn, or partial turn, are needed. These algorithms can beput into two categories, those involving magnets with axial symmetry andthose without axial symmetry. In addition, it is possible to havepractical modalities of operation for symmetrical magnets which takeadvantage of the symmetry to simplify the magnet articulations, and touse fewer numbers of degrees of freedom in them. Three preferredmodalities will be described: (A) is an efficient, highly specific3-degree of freedom navigation for an axially symmetric magnet, with aflow chart for the inversion of the field in the source magnetcoordinates to the field in the patient coordinates shown in FIG. 13;(B) is a more general 3-degree of freedom method which covers the makingof turns; and (C) is a general 5-degree of freedom algorithm by whichthe greater articulation flexibility provides for better handling ofexclusion boundaries in which the magnet cannot move.

(A) 3-Degree of Freedom Navigation for an Axially Symmetric Magnet

It can be seen that one of ordinary skill in the art can extend thespecific information of this example (A), especially the explicitdefinitions and diagrams, in a manner to provide different versions ofthe present means, or any more general modality of navigation by usingdifferent numbers of rotations and/or translations.

FIG. 11 is a diagram showing a patient, a single magnet source ofexternal magnetic field, the location for a small magnet tip to beguided in a medical procedure, and the definition of a few of thecoordinates and vectors to execute the above-described type ofnavigation in one preferred embodiment. At the magnet tip location oroperating point 42 specified by r′ (also by point P) a magnetic field Bis to be applied with given magnitude and orientation to create a turn.

FIG. 12 shows additional useful parameters and defines coordinates forthe single magnet and field point (the operating point represented byposition vector r′) at which the field vector B is to be specified, andwhich is to be provided by the articulated magnet. It also shows planeswhich make the geometric attributes of this motion easier to visualize.

The magnet position in this three degree-of-freedom problem is uniquelyspecified by the offset z_(o) (distance of the center of the coil fromthe closest point of patient anatomy), and the polar and azimuth anglesmade by the magnet symmetry axis z_(m) relative to the translatedpatient coordinate system (x, y, z′) system.

For a coil having axial symmetry this method shows how to make thesearch for one degree of freedom trivial by using an analyticalexpression for one of the variables. This method takes advantage of thefact that the field vector B must lie in the plane defined by thevectors z_(m) and ρ_(m), due to the cylindrical symmetry of the sourcemagnet (either a coil magnet or a permanent magnet).

Referring to FIG. 11 and 12 for a supine patient, the y-z plane ishorizontal, x is vertical, y is horizontal to the patient's right, and zis along the patient body axis. A second set of coordinates is used,where x, y, z′ with origin O′ is displaced along z by an amount z_(o)from the patient origin O shown in FIG. 11. Thus the x,y,z and x,y,z′planes are vertical and are perpendicular to the patient body axis, atthe top of the patients head and through the magnet center,respectively.

The operating point 42 (or P) is at r′ in the x, y, z′ coordinatesystem. θ_(o), φ_(o) are the spherical polar coordinates of B in asystem with polar axis along z′, and azimuthal angle measured from thex,z′ plane. In FIG. 12, B is shown both at its true location P and atthe origin O′ where these angles can be shown clearly. θ_(a), φ_(a) arethe polar and azimuthal angles of the magnet axis z_(m), in the samespherical polar coordinate system as the patient frame, with the polaraxis along z and the azimuth measured in the x,y plane and relative tothe x-axis.

z_(m), ρ_(m) are the cylindrical coordinates of the operating point 42in an axially symmetric magnet coordinate system, corresponding to thevectors z_(m), ρ_(m). The field point at x, y, z′, specified as thevector r′, is identified as P. The point of intersection of a lineparallel to the z-axis and passing through P with the line of projectionof r′ on the x, y plane, is identified as A. The polar angle of r′ inpatient coordinates is identified as θ′. The polar angle of r′ in magnetcoordinates is identified as β. The point on the z-axis at z_(o)+z isidentified as K. There are three parallelograms defining three planes:The first, O′APK is a parallelogram which forms a plane perpendicular tothe x, y plane and going through both the z-axis and the field point P.r′ falls in this plane. The rotation of this plane about the z-axis isby angle φ′ with respect to the x-z plane. The second, O′ρ_(m)Pz_(m) isa parallelogram which forms a plane containing the field point P and theaxes z_(m) and ρ_(m). r′ also falls in this plane and therefore thisvector forms the axis of intersection of the two planes. By itsdefinition z_(m) is the projection of r′ on the axis of the coil. Notonly the field point P, but the field vector B lies in this plane, whichis an axial plane of the magnet (a plane containing a complete fieldline and the magnet axis). r′, and therefore both parallelograms, rotateabout z as the field point changes in azimuth in the patientcoordinates. The second parallelogram is in general tilted relative tothe first. The third plane is the plane formed by B and the line PA.This plane is in general oblique to the first and second planes.

As defined, φ_(a) is a precession angle of the magnet axis, theazimuthal rotation about z (measured from the x,z plane) of the line ofthe projection of vector z_(m) representing the magnet axis, on the x-yplane.

The algorithm is implemented in the following steps (derivation anddetails are given later):

1. Specify coordinates (x, y, z) of a field point in the navigationvolume of the patient.

2. Specify the magnitude of the desired magnetic field B, and a desiredaccuracy for this magnitude.

3. Specify the polar and azimuth angles θ_(o) and φ_(o) of the desired Bvector.

4. Specify an accuracy for the dot product between the specified andcomputed B unit vectors.

5. Search on the magnet azimuth coordinate φ_(a) as follows:

a. For each φ_(a), search on the magnet offset, z_(o).

b. For each pair φ_(a), z_(o), calculate the magnet polar angle, θ_(a),which is required to insure that the B vector lies in the z-r′ plane.

c. Continue the search on the offset z_(o) until the computed coil fieldmagnitude is equal to B to within the desired accuracy.

d. Using this offset, and the set of azimuth and polar magnet angles,compute the B vector at the field point

e. Form the dot product between the computed and specified B vectors.Form the dot product of unit vectors by dividing by the vectormagnitudes.

f. When this dot product is equal to unity to within the specifiedaccuracy, the inverse calculation is complete

6. Calculate the changes in z_(o), φ_(a) and θ_(a) from their presentpositions.

7. Calculate a sequence of these variables which will provide thechanges proportionately.

8. Send the sequence to the magnet articulation device 36 to effect thedetermined movement of the source magnet 38.

In summary, the method searches magnet azimuth and magnet offset,computes a polar angle that insures that the B vector lies in a planecontaining the magnet axis and the field point vector, selects an offsetthat insures the correct magnitude of B, and completes the azimuthsearch when the computed and specified B vectors are aligned in space.

The derivation and details of this Example A are as follows: The vectorsr′, z_(m), and B are given in their polar representations by:r′=r′[sin θ′ cos φ′i+sin θ′ sin φ′j+cos θ′k]  (5)z _(m) =z _(m)[sin θ_(a) cos φ_(a) i+sin θ_(a) sin φ_(a) j+cos θ_(a)k]  (6)B=B[sin θ_(o) cos φ_(o) i+sin θ_(o) sin φ_(o) j+cos θ_(o) k],  (7)

The angles of the position vector r′ are given in terms of its Cartesiancoordinates by:φ′=tan⁻¹(y/x)  (8)θ′=tan⁻¹{[√(x ² +y ²)]/(z+z _(o))},  (9)and,r′=√[x ² +y ²+(z+z _(o))²].  (10)

The polar and azimuth angles θ_(a) and φ_(a) of the magnet axis areunknowns to be determined. The polar and azimuth angles of the B vector,θ_(o) and φ_(o), are specified by the user, or are calculated from itsCartesian representation.

The polar angle θ_(a) can be computed mathematically in terms of theother angles by imposing the condition that the B vector lie in thez_(m)-r′-ρ_(m) plane. This condition is necessitated by the symmetry ofthe coil. It is stated mathematically as the null dot product of B witha vector perpendicular to that planeB·(z _(m) xr′)=0.  (11)Insertion of the defining equations (1) to (3) into (7), and noting thatthe magnitudes of the vectors drop out, we have an equation which can besolved for the tangent of the polar angle:θ_(a)=tan⁻¹{[sin θ′ sin θ_(o) sin (φ′−φ_(o))]/[cos θ_(o) sin θ′sin(φ′−φ_(a))+cos θ′ sin θ_(o) sin(φ_(a)−φ_(o))]}  (12)The field components relative to the magnet are given by:B(r′)=B _(ρ)(ρ_(m) , z _(m))ρ_(m)/ρ_(m) +B _(z)(ρ_(m) ,z _(m))z _(m) /z_(m)  (13)where a numerical coil field algorithm computes B_(ρ) and B_(z), giventhe coordinates z_(m) and ρ_(m). From FIG. 12 the magnitude of the z andρ components of the vector r′ are:z _(m) =r′ cos β  (14)ρ_(m) =r′ sin β,  (15)where the angle β is measured in the z_(m)-r′-ρ_(m) plane and can befound from vector operations to be:cos β=sin θ_(a) sin θ′ cos(φ_(a)−φ′)+cos θ_(a) cos θ′  (16)sin β=√(1−cos²β).  (17)The computed magnitude of the field in magnet components isB=√(B _(ρ) ² +B _(z) ²),  (18)and this expression is used in the algorithm to search the magnetoffset, z_(o), where equations (12) to (17) are used to compute equation(18) for each value of z_(o).

Finally, the search on the magnet axis azimuth is terminated when thespecified B vector and the B vector computed from Equation (13) arealigned in space to within a given accuracy. Appropriate expressions forthe unit vectors in terms of the patient Cartesian coordinates are:

$\begin{matrix}\begin{matrix}{{z_{m}\text{/}z_{m}} = {{\sin\;\theta_{a}\cos\;\phi_{a}i} + {\sin\;\phi_{a}\sin\;\phi_{a}j} + {\cos\;\theta_{a}k}}} \\{{\rho_{m}\text{/}\rho_{m}} = {\left( {r^{\prime} - z_{m}} \right)\text{/}\rho_{m}}}\end{matrix} & (19) \\\begin{matrix}{\;{= {{\left\lbrack {{\left( {{\sin\;\theta^{\prime}\cos\;\phi^{\prime}} - {\cos\;{\beta sin\theta}_{a}\cos\;\phi_{a}}} \right)/\sin}\;\beta} \right\rbrack i} +}}} \\{{\left\lbrack {{\left( {{\sin\;\theta^{\prime}\sin\;\phi^{\prime}} - {\cos\;{\beta sin\theta}_{a}\sin\;\phi_{a}}} \right)/\sin}\;\beta} \right\rbrack j} +} \\{\left\lbrack {\left( {{\cos\;\theta^{\prime}} - {\cos\;{\beta cos\theta}_{a}}} \right)\sin\;\beta} \right\rbrack k}\end{matrix} & (20)\end{matrix}$

The specified and computed unit vectors are obtained from equations (7)and (13) by dividing by the specified field magnitude and fieldmagnitude computed by Equation (18), respectively. When their dotproduct is equal to unity, within the specified accuracy, the azimuthsearch is complete.

The solution offset, polar and azimuthal angles z_(o), θ_(a), and φ_(a)are then used to articulate the magnet to acquire the desired field B.

FIG. 13 is a flow chart of a program which executes the algorithm justpresented to provide the inverse calculation for articulating a magnethaving axial symmetry. A preferred embodiment of a more general searchwhich allows an incremental proper rotation of a field vector ispresented below in example (B). An outline of an embodiment for ageneral 5-degree-of-freedom search is also presented below in example(C). One versed in the art will see how to modify these to provideinversion algorithms to articulate a magnet with any number of degreesof freedom greater than 3.

(B) Navigation with 3-Degree of Freedom Searches

The algorithm outlines a method which operates directly withtransformation matrices, but requires a full 3-parameter search.

Magnet Insertion

1. Locate the current magnet tip location, r′ (i.e. the operating point42 or P) in the patient frame.

2. Input the desired starting field direction, B, in patientcoordinates.

3. Using appropriate transformations, and a search sequence, calculatethe necessary magnet axis rotational angles, φ and θ, and translationaxis position to achieve B at r′.

4. Execute magnet axis rotations φ and θ.

5. Execute translation to calculated position.

After the source magnet has been inserted

1. Locate the current magnet tip location, r′, in the patient frame.

2. Translate the magnet along the z-axis to bring the operating point 42or P where the magnet tip 46 is located, to the desired field strengthline of the magnet.

3. Calculate the desired new magnetic field direction B₂ in patientreference frame at the operating point P or 42 where the magnet tip 46is located.

4. Input the new desired magnetic field direction, B₂, in patientcoordinates.

5. Create a set of vectors in the patient reference frame that link B₁to B₂ at the operating point 42 or P that lie in the plane created by B₁and B₂.

6. Calculate the necessary magnet axis rotations, φ and θ, andtranslation that produces the set of vectors found in step #5.

7. Execute movement with the 3 variables synchronized.

In a practical device for implementing the method of example (B), suchas the one shown in FIGS. 7A and 7B, the azimuthal rotation might belimited to 360°, the polar rotation limited to 180°, and the Z-axistranslation might be limited to 8.5 inches to about 14.5 inches. Motionis selected to avoid possible problem with navigation due to rotationalstops in azimuthal direction.

(C) Navigation with 2 Rotational and 3 Translational Degrees of Freedom

This outlines a method of using two additional translational motionswhich can give flexibility to avoiding interferences with patient andimaging equipment and beams. Such a method might be implemented by thedevice shown in FIG. 7C. By choosing specific x and y axis translationsat the outset, the problem again becomes completely determined. If otherconstraints are more valuable in a specific application, these can bereplaced.

1. Locate the current magnet tip location, P

2. Translate in the x y plane (x-axis and y-axis) such that the tipposition and the center of the magnet coil define a line parallel to thez-axis of translation.

3. Translate along the z-axis to bring the current tip location, P, tothe desired field strength line.

4. Calculate the magnetic field direction, B₁, at the tip location P.

5. Input the desired new field direction, B₂.

6. Create a set of field vectors that link B₁ to B₂ at P, and which liein the plane of B₁ to B₂.

7. Calculate the necessary magnet rotations, φ and θ, and translation(z-axis only), for the set of vectors created in step 6.

8. Execute source magnet movement.

Use of Gradients

Navigation in accordance with this invention can be conducted in such away as to use the source magnets to pull the medical device in additionto orienting the distal end of the medical device. Magnetic force isgenerated by the rate of change of magnetic field strength withposition. This is commonly called a “magnetic gradient” even though avector magnetic field does not have a gradient in the usual mathematicalsense. As is well known to one of ordinary skill in the art, a magneticfield is a vector field, and a gradient operates only on a scalar field,that is a scalar function of position. What is usually meant by gradientis not gradient of the magnetic field, but the gradient of a scalarproduct of the magnetic moment vector m of the tip, and the magneticfield vector B at its location, i.e., (m·B). What is intended here, andgenerally in magnetic work, is the application of the force equationF=∇(m·B)  (21)Assuming a small magnetic tip 46, the moment can be treated as a point.This assumption is adequately met when the magnetic field changes over adistance appreciably larger than the size of the magnet tip. Thus thegradient operator acts on the scalar product m·B, the position dependentproduct of the magnet tip moment projected on the field B, at any givenpoint The direction of this force need not be along either the fielddirection B or the direction of the moment m. Rather it is in thedirection in which the product m·B changes most rapidly.

It is the purpose of this aspect of the invention to navigate a magneticmedical device with a magnet tip safely to a location and orientation ina patient so that the magnetic gradient which falls at that point willpull the tip in a desired direction. FIG. 14 shows a cross sectioncontaining the axis of a typical coil source magnet 38 with a number ofits magnetic field lines. The arrows on the field lines show thedirection of the magnetic field B at points along each line. Inaddition, the gradient of the field is shown in two locations, at pointsA and B, by double arrows. The directions of the arrows show thedirections that a free small magnet would be pulled at those twolocations. The direction of pull on a free magnet is in the direction inwhich the field lines are becoming denser, which is also the directionin which the field is increasing in strength. This is because a freemagnet will align its moment with B, and remain aligned as it is pulled.

Thus the product m·B becomes simply the arithmetic product of themagnitudes of the two vectors, mB. But in practice a small magnet tip 46on a magnetic medical device is not totally free, rather it is somewhatrestrained by the device with which it is associated, as well as anysurrounding issue with which it is in contact. For example, catheters,guidewires, and electrodes etc. all have inherent stiffness that wouldrestrain the alignment of the magnet tip with the field direction, inwhich case the product m·B will be somewhat smaller than mB, which isthe maximum possible value.

In FIG. 14, a free magnet tip 46 at point A will be oriented with itsmoment aligned along the field which is along the axis of the sourcemagnet 38, and the magnet will be pulled along the same direction. Thisis the “longitudinal gradient” or alternatively the “longitudinalfield.” It is also sometimes called an “axial gradient” At point B thefree magnet tip 46 will have its moment m aligned along B and thereforeparallel to the magnet axis, but the gradient will pull the magnet tiptowards the source magnet as shown by the arrow, ie., perpendicular tothe source magnet axis. This is called a “transverse gradient”, oralternatively a “transverse field.” In some medical applications (e.g.,pulling a linear electrode to an inner wall of a heart chamber, orpulling magnetic embolic material more smoothly towards an inner wall ofan aneurysm) such a transverse gradient has been found to beadvantageous.

According to this aspect of the invention, the magnetic navigation issupplemented by the application of the magnetic gradient. In someinstances the application of the magnetic gradient assists innavigation, in other instances, the gradient is not applied to assistnavigation, but to otherwise exert a pulling force on the magneticmedical device.

There are many instances where it would be desirable to exert a pullingforce after a magnetic medical device has been navigated to a particularposition in the body. For example, in the case of treating aneurysms, amagnetic pulling force could be applied after navigation of a magnet tipto a given location, for pulling magnetic embolic materials into ananeurysm. (The magnetic medical device may or may not be removed fromthe area before applying the pulling force). Either a transverse orlongitudinal gradient may be used. If no subsequent navigation orsignificant turning of the orientation of the magnetic medical device isrequired, the computer processor 22 which controlled the initialnavigation will have information not only about the orientation of themagnet tip 46, but about the orientation of the source magnetic fieldand gradient. That is, the processor will have information whether, atthe operating point 42, the gradient is transverse or longitudinal.According to this aspect of this invention, the physician will, at thestart of the procedure, input the desired method of using the gradient,and therefore at the completion of navigation (and after removal of themagnet tip, if necessary) the source magnet 38 will be oriented so thatthe gradient is in the desired direction.

At this point, a gradient must be established in the desired directionof pulling (e.g., the back wall of an aneurysm in an embolizationprocedure, or the wall of a heart chamber in an EP (electrophysiology)procedure). The processor 22 will have information about the currentstate of the magnetic field and gradient. Given the desired state of therelative directions of magnetic field and gradient, the processor candetermine and direct a movement of the source magnet for the purpose ofchanging the direction of the gradient relative to the direction of thefield, or vice versa. This relative movement between gradient directionand field direction is called a “gradient turn”.

FIG. 15A shows a cross section of an aneurysm with a magnetic field Brepresented by field lines pointing away from the back wall of theaneurysm, and a magnetic gradient represented by a double arrow,pointing toward the back wall of the aneurysm. In certain embolizationprocedures, it is desirable that the applied magnetic field be parallelto the neck of the aneurysm and perpendicular to a magnetic gradientthat is oriented toward the back wall of the aneurysm. This builds alayered embolism in the aneurysm. As shown in FIG. 15B, after a gradientturn the magnetic field B represented by field lines pointing parallelto the neck of the aneurysm, is now perpendicular to magnetic gradient,represented by the double arrow, pointing toward the back wall of theaneurysm. While it is apparent from FIG. 14, and equation (21) what thegradient direction will be at these starting and ending locations, it isnot apparent how the field and gradient directions relate at theintervening locations, nor how to use equation (21) to determine thegradient changes during that transition. The execution of a “gradientturn” above, will require a knowledge of the projection of B on m.

The requirement, then, is for the processor 22 to determine themovements of the source magnet 38 necessary to perform the gradient turnin the coordinate system of the patient. FIG. 14 shows a gradual changein the spacing of lines moving from a longitudinal gradient at point Ato a transverse gradient at point B. That is, there can be a gradualchange in the gradient of the scalar product m·B since m is fixed inmagnitude and the line spacing is proportional to the magnitude of B. Asdiscussed above, the navigation program implemented by the processorcontains either an equation or a lookup table for the source magneticfield B of the magnet in the source magnet coordinate system. Thelocation of the magnet tip 46 in the patient coordinate system istransformed into the source magnet coordinate system as described inearlier, so that B is known at the operating point 42 in the patientcoordinate system from a further inverse transformation. The force Ffrom equation (1) is determined from this information, knowing m, forthe current source magnet position and orientation, and for a series oftrial rotations and translations. The only additional requirement isknowledge of, or an assumption of, the direction of m during thegradient turn. From these trial calculations, the choice of a gradientturn of the source magnet is made in the same manner as was describedfor a safe navigation turn above. If, due to limitations in accuracy,there is significant error in assumed change in the direction of m, itmay or may not be necessary for a locator or imaging system to measurethe change in direction and update the processor.

In all but unusual conditions, the procedure described above isconceptually simple, since m·B varies as mB cos θ, where θ is the anglebetween m and B. The direction and magnitude of m in the patientcoordinate system will not change significantly in the types ofnavigation likely to be used. However, due to the transformationsbetween coordinate systems the quantity cos θ will change from 1 to 0 asthe source magnet is moved (in the example illustrated in FIGS. 15A and15B) so that the transformed operating point 42 moves from a point onthe axis of the source magnet axis to a point on its equatorial plane inthe source magnet coordinates, that is θ goes from 0 degrees to 90degrees. In the process, the quantity B will change in the patient,since the side field of the source magnet is less than the axial fieldof the source magnet, at a given distance. This may be not important,since the field strength for pulling a magnetic material into ananeurysm will be separately input by special requirements. To fulfillthe needed change in the strength of B, the source magnet 38 will betranslated closer to or further from the operating point 42 in thepatient.

In another embodiment, such as the orienting and pulling of amagnet-tipped electrode against an interior heart chamber wall, it maybe necessary to retain an orienting magnetic field in a directionapproximately parallel to the wall, while exerting a pulling gradientapproximately towards the wall. This may occur in a manner in which themagnet tip or tip ensemble on the electrode have in their design thecapability of responding directly to a transverse gradient, and notresponding in that manner to a longitudinal gradient. Special tipdesigns are needed, such as described in U.S. patent application Ser.No. 09/311,686, filed May 13, 1999, for Magnetic Medical Device andMethod of Navigating Magnetic Medical Devices with Magnetic Fields andGradients, incorporated herein by reference. In such a case, informationspecific to the design of the particular magnetic tip 46 will have beenentered in the processor 22 at the start of the procedure. The magnetictip 46 will be navigated to the procedure location, such as a chamber ofthe heart, in a manner similar to that of a simple magnet tip. When thetip has been navigated to the desired point, the source magnet can beturned so as to progressively move the gradient from longitudinal totransverse, while holding the tip against the wall, as described above.While changing the gradient direction, the magnet tip 46 is held towardsthe wall by applying a torque with the magnetic field direction. Themagnet tip 46 is held against the wall in this manner while the gradientis being applied to pull the magnet tip toward the wall. In essence,there is a continuous transition from a guidance-dominant situation to apull-dominant situation.

One embodiment of system for carrying out navigations in accordance withthe methods of this invention is indicated generally as 200 in FIGS. 7Aand 7B. The system 200 comprises a patient bed 202 for supporting thepatient, an imaging system 204 for providing images of the operatingregion within a patent on the patient bed 202, and a magnet system 206for projecting magnetic fields and gradients into the operating regionin a patient on the patient bed 202.

The imaging system 204 comprises a C-arm apparatus 208, mounting twopairs of imaging beam source 210 and imaging plates 212, which arepreferably mutually perpendicular. The C-arm apparatus includes agenerally L-shaped support 214 that is mounted on base 216 for pivotingabout a generally vertical axis, an intermediate support 218 that ismounted on L-shaped support for rotation about a generally horizontalaxis; and a C-shaped bracket 220 that is mounted on the intermediatesupport for rotation about the central axis of the C-shaped bracket.

The magnet system 206 comprises a source magnet 222 and an articulationdevice 224 for translating and rotating the source magnet 222. Thesource magnet is preferably a superconducting electromagnet, withassociated cryocooler 226. The housing conventionally used is omitted toshow the configuration of the magnet. The articulation device 224provides movement of the magnet 222 with three degrees of freedom (tworotations and one translations). The articulation device 224 comprises abase 228 that is mounted on tracks 230 for translation toward and awayfrom the patient bed, thereby allowing translation of the magnet 222toward and away from the operating region within a patient on thepatient bed 202 (i.e. along the z axis as described above). Thearticulation device 224 includes a C-shaped arm 232, that is mounted onthe base 228 for rotation about a first generally horizontal axis, whichallows a first rotation of the magnet 222. The magnet 222 is alsomounted to the C-shaped arm 232 for rotation about a second axisgenerally perpendicular to the first generally horizontal axis, whichallows a second rotation of the magnet.

The movement of the base 228 on the tracks 230, rotation of the C-shapedarm 232 relative to the base, and the rotation of the magnet 222relative to the C-shaped arm provides magnet motion with three degreesof freedom, and each of these movements can be controlled by amicroprocessor as described herein, to project a desired magnetic fieldand or gradient into an operating region within a patient on the patientsupport.

FIG. 7B shows the system 200 with a surface 234 of constant fieldstrength projected around the magnet 222. In navigations using thisconstant field strength, it is apparent there is at least onesignificant exclusion zone surrounding the location where the cryocooler226 projects through the surface 234. Rotations and translations thatwould attempt to bring this exclusion zone to the operating regionwithin the patient must be prohibited, because the cryocooler wouldstrike the patients. Other rotations and translations that would bringthis exclusion zone into contact with other structures in the operatingroom, for example with the imaging system 204 or the articulation device224, or interfere with the imaging beams from the imaging system 204,must also be prohibited as described below.

Another embodiment of system for carrying out navigations in accordancewith the methods of this invention is indicated generally as 300 inFIGS. 7C through 71. The system 300 comprises a patient bed 302 forsupporting the patient, an imaging system 304 for providing images ofthe operating region within a patient on the patient bed 302 patient,and a magnet system 306 for projecting magnetic fields and gradientsinto the operating region in a patient on the patient bed 302.

The imaging system 304 comprises a C-arm apparatus 308, mounting twopairs of imaging beam source 310 and imaging plates 312, which arepreferably mutually perpendicular. The C-arm apparatus includes agenerally L-shaped support 314 that is mounted on base 316 for pivotingabout a generally vertical axis, an intermediate support 318 that ismounted on L-shaped support for rotation about a generally horizontalaxis; and a C-shaped bracket 320 that is mounted on the intermediatesupport for rotation about the central axis of the C-shaped bracket.

The magnet system 306 comprises a source magnet 322 and an articulationdevice 324 for translating and rotating the source magnet 322. Thesource magnet 322 is preferably a superconducting electromagnet, withassociated cryocooler 326, the magnet is surrounded by a housing 328.The articulation device 324 provides movement of the magnet 322 withfive degrees of freedom (three rotations and two translations). Thearticulation device 324 comprises a base 330 that is mounted on tracks332 for translation toward and away from the patient bed 302, therebyallowing translation of the magnet 322 toward and away from theoperating region within a patient on the patient bed 302 (i.e., alongthe z axis as described above). A turntable 334 is mounted on the base330 for rotation about a generally horizontal axis. The turntable 334has a track 336 extending diametrically across it for slidably mountinga support arm 338, so that the support arm can translate within thetrack. The magnet is mounted on the end of the support arm. Morespecifically a C-shaped arm 340 is mounted on the end of the support arm338, for rotation about a first axis. The magnet 322 is mounted to theC-shaped arm 340 for rotation about a second axis generallyperpendicular to the first axis.

The movement of the base 330 on the tracks 332, rotation of theturntable 334 relative to the base, the translation of the support arm338 relative to the turntable 334, the rotation of the C-shaped arm 340relative to the support arm, and the rotation of the magnet relative tothe C-shaped arm provides magnet motion with five degrees of freedom,and each of these movements can be controlled by a microprocessor asdescribed herein, to project a desired magnetic field and or gradientinto an operating region within a patient on the patient support.

FIG. 7E shows the system 300 with a work envelope 350 surrounding thepatient, defining the volume in which the articulation device 324 cantranslate the magnet 322. FIG. 7F shows the system 300 illustrating therange of motion of magnet, illustrating a maximum 360 degree rotation ofthe magnet 322 about the C-shaped 340 (not shown in FIG. 7F), and amaximum 180 degree rotation of the C-shaped arm 340, relative to thesupport arm 338.

FIG. 7G shows the system 300 illustrating a magnet work envelope 352within which the magnet 322 can be translated and the sweep volume 354that must be clear to accommodate the cryocooler 324 as the C-shapedsupport arm 340 and the magnet 322 rotate for a given translationalposition of the magnet in the work envelope 352. FIG. 7H shows thesystem 300 illustrating a rotation of the magnet 322 to provide accessfor the magnet to project the desired magnet field and/or gradient inthe operating region in a patient on the patient bed 302. FIG. 71 showsthe system 300 and illustrates the clearance between the work envelopearound in the patient in which the magnet 322 moves, and the support forthe imaging system.

In navigations using the system 300, it is apparent there aresignificant limitations on the positions and orientations of the magnetto avoid contact with the patient, other equipment in the operatingroom, and imaging beams from the imaging apparatus. These limitationscan be addressed using exclusion zones, as described in more detailbelow.

Use of Exclusion Zones

For some of the procedures for which the magnetic navigation method ofthe present invention may be employed, there will be congestion in theregion surrounding the patient, making it difficult to articulate asource magnet in ways desired to provide guiding fields in all neededdirections and at required magnitudes. Primarily, the magnet and itsaccoutrements cannot be translated or rotated in such a way that theyimpinge upon the patient or any of surrounding medical equipment,including for example the patient bed and the imaging equipment, orinterfere with the imaging beams. The processor 22 can control themovement of the source magnet 38 so that the interference does notoccur, and can even anticipate interferences for a planned path of anumber of turns for the navigated object.

The processor 22 can determine the necessary safe and efficient steps,or component parts of a step, in a path of navigation. Each such steprequires rotation and/or translation of the source magnet, and theprocessor calculates these by transforming the desired step, in thepatient reference frame, to its geometrical counterpart in the sourcemagnet reference frame, and calculates efficient and safe source magnetmotions to accomplish the field changes in the patient reference frame,as described herein. The following steps can be implemented to avoidthese interferences:

The geometric “edge” of the patient, imaging equipment, etc. on the sidefacing the source magnet 38, can be thought of as a somewhat complex“sheet”. This sheet can be defined in the coordinates of the patientreference frame by a set of vectors from the origin of that frame toappropriate points on the “patient sheer”. The number and distributionof these vectors can vary, depending on the complexity of the sheet andthe desired geometrical resolution in its description. Nevertheless,they can be stored in the processor memory, for example as a look-uptable, or instead as a set of equations for geometrical objects.

Similarly, a “source magnet sheet” can be described in the articulatable(moveable) magnet reference frame as a set of vectors in thosecoordinates. On any anticipated move of the source magnet 38, theprocessor 22 can test for overlap or touching of the two sheets bytransforming either one to the reference frame of the other. Moreover,the processor can determine (and present on a display if desired) theclosest distances if there is not yet an interference.

When these “tests” are applied to an articulation which is used to placea vector magnetic field in the patient, there are a number of ways ofaccomplishing the desired directional change of the magnetic field, somemore geometrically efficient than others. The injection of interferenceavoidance as a constraint on possible articulations must then becombined with the vector field properties of the magnet in testing foralternate articulation in any given desired move.

The specific steps involved in this combination will depend on thenumber and types of degrees of freedom of the articulation mechanism 36.Specifically: (A) A 3-degree of freedom system will have no availableredundancy for a single move. In such cases multiple moves must beplanned ahead for interferences, if necessary using tolerances in theprovided field direction. (B) Systems with 4 or more degrees of freedomcan have remaining choice(s) for each specific move. Among other things,these choices offer different angles for the “magnet sheet” to approachthe “patent sheet”. They can offer alternate articulations for a givenplanned path without using field direction tolerance.

The way this can be put into the navigation trial solutions is shown inFIG. 10, in which “trial” moves shown as P_(i) and P_(n), etc. arerotations and/or translations of the source magnet 38 which will be ableto make a given direction change of the field B in the patient (givensufficient number of degrees of freedom) at the point operating point 42where the magnet tip 46 is to be navigated, while maintaining a constantfield magnitude B.

Given the patient and source magnet sheets as previously described, theprocessor 22 will be able to determine regions of these P_(i) directionswhich are not permissible for a proposed tum, and thereby restrict thesolution set. It is to be understood that each of these vectors P_(i)corresponds to the same or nearly the same turn of B in the patent, andthey differ only in the way they use the excess degrees of freedom ofthe articulation mechanism 36. (A result of this will be a change in the“efficiency” of the turn which can be defined as the amount of turningand translating of the source magnet to provide such a safe and correct(planar) turn of the vector B in the patient.)

1. A method of turning a medical device, having a magneticallyresponsive element associated with its distal end, at an operating pointwithin an operating region inside a patient's body from an initialdirection to a desired final direction, through the movement of at leastone external source magnet, the method comprising: moving the at leastone external source magnet in such a way as to change the direction ofthe distal end of the magnetic medical device from the initial directionto the desired final direction without substantial deviation from theplane containing the initial direction and the desired final direction.2. The method according to claim 1 wherein the movement of the at leaseone source magnet comprises translations and rotations.
 3. The methodaccording to claim 2 wherein the movement of the at least one sourcemagnet includes translation in one direction and rotations in twodirections.
 4. The method according to claim 1 wherein the at least onesource magnet is moved in such a way as to maintain a substantiallyconstant magnetic field strength at the operating point.
 5. The methodaccording to claim 1 wherein the step of moving the at least oneexternal source magnet includes moving the at least one external sourcemagnet to cause the distal end of the magnetic medical device tosuccessively align with a plurality of intermediate directions in aplane containing the initial direction and the desired final direction.6. The method according to claim 5 wherein the movement of the at leastone source magnet comprises translations and rotations.
 7. The methodaccording to claim 5 wherein the at least one source magnet is moved insuch a way as to maintain a substantially constant magnetic fieldstrength at the operating point.
 8. A method of turning a medicaldevice, having a magnetically responsive element associated with itsdistal end, at an operating point within an operating region inside apatient's body, from an initial direction to a desired final direction,through the movement of at least one external source magnet, the methodcomprising: moving the external source magnet to cause the distal end ofthe magnetic medical device to successively align with each of aplurality of intermediate directions and the desired final direction,while maintaining a substantially constant magnetic field strength.